I have recently been investigating the use of Relative Positional Precision (RPP) to quantify the precision of the dimensions shown on my surveys. So I decided to start running RPP error analysis on some of my recent surveys. The standard that I am trying to meet is the ALTA 0.07'+50ppm standard. Unfortunately, my last survey did not meet this standard (according to my least squares adjustment program) and I am trying to understand why.
Here is a sketch of my observations. I am holding 101 and 102 as control. My first setup is on 101 backsighting 102. I then traverse to 109, then 178 and close to 102 (no closing angle was observed at 102). Along the way I took sideshots to monuments. All of the traverse and sideshots angles were taken direct and reverse.
Here are my adjustment parameters:
Here are my standard errors, 95% error ellipses and RPP report (showing failure on all specified monument pairs):
Here are my statistics (notice that I am right down the middle on the chi squared test):
Link for entire least squares adjustment report.
So why did I fail? One thing I noticed was that while the standard errors on my points looked pretty good (on average 0.02'), when the confidence interval was pushed up to 95% they didn't look so good anymore and the RPP report reflected that. Only thing that I can think of is the 95% confidence stats are punishing me because I did not have more degrees of freedom (i.e. more redundant measurements).
95% error estimates are basically twice the standard error estimates (68%). I think Surv Net is boogering the 95% calculation. For instance you have a standard error on 103 in N of 0.046. The 95% error should be roughly double at .092 however the 95% semimajor axis (think radius) is 0.199. This would make sense as the total diameter 0.092 x 2 = 0.184 but not as the semi major axis.
Just out of curiosity, can you run the relative inverse test at 68% and cut the allowable tolerance in half 1cm + 25ppm?
I wouldn't take these results to the bank but it might reveal the issue.
First you need to understand what the Chi-Square test is and what it means.
All that test does is compare the relative amount of error you expect vs the relative amount of error in your data. You can take bad expectations and compare with good data and fail this test. You can take bad expectations and bad data and pass the test. The real trick is figuring out what amount of error is reasonable to expect for your equipment, personnel and procedures.
I think the real key to why the data set you posted doesn't meet the ALTA standard is the very low degrees of freedom. You must have redundant data to allow a Least Squares adjustment. The more redundancy you have the better. You are going to find it very difficult to pass the ALTA standard if you just set up a standard traverse loop and measure everything one time. The degrees of freedom measures the number of measurements beyond what is minimally required to get an answer.
If I gave you two side distances of a triangle and one angle, you could calculate the remaining side and two angles. But you would only have one way to do so. Thus, zero degrees of freedom. If I gave you two side distances and two angles, you would have to decide which data to use in calculating the missing information. What the software does is calculate all the possibilities and then compares the answers to see how they match. You need more data.
Larry P
I still miss it, but not by as much. One thing I do notice is that the 68% confidence interval numbers are substantially different than the standard error numbers. I seem to remember something about the degrees of freedom factoring into the confidence interval numbers, but I would expect the 68% numbers to be close to the standard errors. Am I missing something here?
Maybe bumping up your a-priori error estimates (centering and control coordinates) will give you a more favorable result.
> I have recently been investigating the use of Relative Positional Precision (RPP) to quantify the precision of the dimensions shown on my surveys. So I decided to start running RPP error analysis on some of my recent surveys. The standard that I am trying to meet is the ALTA 0.07'+50ppm standard. Unfortunately, my last survey did not meet this standard (according to my least squares adjustment program) and I am trying to understand why.
The easy first thing to change is the line that you are using for azimuth control, unless you actually determined the azimuth of the short line by observation. If you can choose some other line, such as 107-177, designate the azimuth of the longest line between boundary markers tied in the network. You should see a significant improvement.
The target centering error of +/-0.01 ft. is loose for high-quality surveying. Have you tested your centering method to determine that value or is that just a guesstimate? I'd be trying to hold target centering to under 0.003 ft. (< 1mm). You shouldn't have any difficulty doing that with a prism pole fitted with 8' or 10' level vial. With a tribrach on tripod, it should also be a snap if the optical plummet is in good adjustment.
The value of 0.005 ft. (1.5mm) for standard error of target centering is way too large unless the optical plummet is out of whack or no care is being taken. A standard error of 0.001 ft. should be more like it for centering an instrument with a rotatable optical plummet.
Good points, Larry. Degrees of freedom = 3 is the lowest you can get on a closed traverse, and means you didn't set up on the closing point and turn the closing angle. Adding the closing angle, a foresite distance, and a vertical angle will get you to 6 degrees of freedom. Also, adding the backsite distances and vertical angles into the LSA data file, would get you at least another 8, for a total of 14 degrees of freedom. There are simple things you can do to increase you degrees of freedom, and it will help the confidence in the solution a lot.
> Good points, Larry. Degrees of freedom = 3 is the lowest you can get on a closed traverse, and means you didn't set up on the closing point and turn the closing angle. Adding the closing angle, a foresite distance, and a vertical angle will get you to 6 degrees of freedom. Also, adding the backsite distances and vertical angles into the LSA data file, would get you at least another 8, for a total of 14 degrees of freedom. There are simple things you can do to increase you degrees of freedom, and it will help the confidence in the solution a lot.
I ran a couple of my old jobs where I ran a traditional traverse loop and they for the most part passed the test, but it only added one more degree of freedom when I observed the closing angle.
Yeah, it's tricky how degrees of freedom work.
If you only added the closing angle, then that is only one redundant piece of information, and would only increase the DoF by 1.
What I'm saying is that each bit of redundant information you can add will increase the DoF by 1. So if you turn that (1) last angle, (2) measure the foresite distance, and (3) foresite VA, that adds 3 more DoF.
You can also increase your DoF by going through your raw data, finding the measured backsight distances, and adding those into the mix. Some people might think it's a good idea to average the foresite and backsight distances, and just put in one number, but I don't think so. Those are two independent measurements that verify your accuracy, and add real redundancy to your data set, so include those distances and VAs as redundant data, it will help your adjustment results.
Open traverse results are better???
Well, I decided to run the traverse as open (renumbered the closing tie to 102 to be 196) and here are the results.
The program can't do an adjustment, so i assume it is just using my error estimates to compute the error ellipses. Most of my connections passed.
It still says I have one degree of freedom (maybe the distance I measured between the control points).
> Maybe bumping up your a-priori error estimates (centering and control coordinates) will give you a more favorable result.
Tried that. Didn't help much.
If that is the case, Carlson's SurvNET is not picking up on it. When I observed the closing angle, I also shot the distances and measured the vertical angles. Yet it still only added one degree of freedom. Also, with the way I shoot sets, I measure all of the distances twice and the backsite distance gets measured twice for every set I turn.
>95% error estimates are basically twice the standard error estimates (68%).
That's for a 1-dimensional gaussian normal variable. For two dimensions, if the program is set up to take the standard errors you provided as gospel, the Rayleigh distribution would say 2.448 times.
Your LS program is probably re-estimating your standard errors from the goodness of fit using the F-distribution, by applying a factor times your std err numbers times the "std error of unit weight".
With a large number of degrees of freedom, that case converges to the Rayleigh case. With small degrees of freedom, the confidence in that re-estimation is low and the factor times your standard errors has to be large to gain confidence.
DoF factor for 95%
1 19.98
2 6.16
3 4.37
4 3.73
5 3.40
10 2.87
15 2.71
20 2.64
30 2.58
inf 2.448
I had a thread months ago where someone pointed this stuff out to me. I'm not sure whether the commercial programs are consistent on which approach they report. I think Star*Net defaults to believing the standard errors you provide, so long as you pass the Chi-sq test. Wolf and Ghilani text uses the F-distribution approach.
> I had a thread months ago where someone pointed this stuff out to me. I'm not sure whether the commercial programs are consistent on which approach they report. I think Star*Net defaults to believing the standard errors you provide, so long as you pass the Chi-sq test. Wolf and Ghilani text uses the F-distribution approach.
Yes and the Star*Net approach is certainly the one a surveyor would want to use if he or she had realistic values for the various standard errors used in weighting the observations (as should be the case). In that situation, the standard error estimates are based upon an infinite number of degrees of freedom and may be treated as having no uncertainties.
In the case where the standard errors are unknown quantities to be derived from the adjustment, where there aren't enough redundant observations to do that well, the uncertainties in the derived values can be ugly.
It's much, much more efficient to test the equipment to determine the standard errors, use methods and procedures to realize them in the field, and base the adjustment upon those values. The chi square test then is properly simply a validation of the a priori weights.
> Here are my adjustment parameters:
>
>
One thing that I find genuinely odd about that software (Carlson?) is how it wants to divide the standard errors of angles into "pointing" and "reading" components. Considering that manufacturers don't specify the performance of their theodolites and total stations in terms of standard errors of "reading" it seems more like a throwback to the days of optical instruments with micrometers that might be set multiple times to estimate the micrometer reading error.
Star*Net's approach of simply assigning standard errors to angles and directions without trying to break out different components strikes me as superior. Those are the value that can be derived via the DIN and ISO test procedures, after all.
I haven't actually run your numbers, so my post above may or may not be on target for your program.
Another thought - try separating the horizontal and vertical adjustments. It looks like it is complaining about more verticals than horizontals, so maybe that will lead you to finding a problem.
Star*Net Input File - Why did I fail?
In case anyone would like to adjust Bowtie Surveyor's project in Star*Net, here is the input file.
Note use of From-At-To angle format.
Note also that the bearing from 101 to 109 has been used to fix the orientation of the survey instead of holding two coordinates fixed.
[pre]
# Bow Tie Survey Project
C 101 4982.039 5037.077 ! !
C 102 4951.355 5181.797 * *
B 101-109 S4-36-32E !
M 102-101-103 348-23-01.5 487.597
D 101-102 147.935
M 102-101-105 217-59-32.0 56.085
M 102-101-106 353-09-07.5 171.296
M 102-101-107 048-03-00.0 10.124
M 102-101-108 157-36-51.0 38.731
M 102-101-109 073-25-08.0 239.780
M 101-109-177 207-47-08.0 39.541
M 101-109-178 097-09-21.0 122.179
M 109-178-102 088-20-42.5 213.806
M 109-178-219 226-08-24.0 42.134
.REL 107-177 177-219 219-106 106-107
[/pre]
Star*Net Input File - Why did I fail?
Running the adjustment with these settings:
[pre]
Instrument Standard Error Settings
Project Default Instrument
Distances (Constant) : 0.005000 FeetUS
Distances (PPM) : 5.000000
Angles : 10.000000 Seconds
Directions : 3.000000 Seconds
Azimuths & Bearings : 4.000000 Seconds
Centering Error Instrument : 0.002000 FeetUS
Centering Error Target : 0.010000 FeetUS
[/pre]
produces this statistical summary:
[pre]
Adjustment Statistical Summary
==============================
Convergence Iterations = 2
Number of Stations = 11
Number of Observations = 22
Number of Unknowns = 20
Number of Redundant Obs = 2
Observation Count Sum Squares Error
of StdRes Factor
Angles 10 2.797 1.754
Distances 11 0.864 0.929
Az/Bearings 1 0.000 0.000
Total 22 3.660 1.353
The Chi-Square Test at 5.00% Level Passed
Lower/Upper Bounds (0.159/1.921)
[/pre]
This indicates that there may be (but not definitely is) a problem with the angles, possibly either a blunder or a standard error that was too small.
These are the adjusted angles
[pre]
Adjusted Angle Observations (DMS)
From At To Angle Residual StdErr StdRes
102 101 103 348-23-01.50 0-00-00.00 17.78 0.0
102 101 105 217-59-32.00 -0-00-00.00 41.73 0.0
102 101 106 353-09-07.50 -0-00-00.00 20.97 0.0
102 101 107 48-03-00.00 -0-00-00.00 208.13 0.0
102 101 108 157-36-51.00 0-00-00.00 57.50 0.0
102 101 109 73-25-14.14 0-00-06.14 19.40 0.3
101 109 177 207-47-08.00 -0-00-00.00 55.12 0.0
101 109 178 97-09-50.02 0-00-29.02 21.79 1.3
109 178 102 88-21-03.82 0-00-21.32 22.20 1.0
109 178 219 226-08-24.00 0-00-00.00 54.17 0.0
[/pre]
and these are the estimated relative positional uncertainties at 95% confidence:
[pre]
Relative Error Ellipses (FeetUS)
Confidence Region = 95%
Stations Semi-Major Semi-Minor Azimuth of
From To Axis Axis Major Axis
106 107 0.058982 0.038718 1-43
106 219 0.059115 0.049119 11-09
107 177 0.046309 0.036731 173-28
177 219 0.051469 0.043987 45-40
[/pre]
Star*Net Input File - Why did I fail?
Kent,
Can you run it holding only point 101 fixed and the bearing you specified.
Thanks,